Is it legal for an employer to deny the use of accrued sick time?

Question Details: I work part-time for an organization in the state of MA which is eligible for paid sick leave 30 employees and have accrued 30 hours of sick-time since starting. I have been told that since we are not guaranteed specific shifts, and our shifts are determined based on other employee availability, that I cannot use this time. We are told instead that if we are sick we just have to find another employee to cover our shift and this time will go unpaid. Are there any circumstances where this could be allowed?

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